Complex Analysis And Related Topics
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Complex Analysis and Related Topics
This volume, addressed to researchers and postgraduate students, compiles up-to-date research and expository papers on different aspects of complex analysis, including relations to operator theory and hypercomplex analysis. Subjects include the Schrödinger equation, subelliptic operators, Lie algebras and superalgebras, among others.
Complex Analysis, Operators, and Related Topics
This volume is devoted to some topical problems and various applications of operator theory and its interplay with modern complex analysis. It consists of 30 carefully selected surveys and research papers. The main subjects of the volume include: · free interpolation by analytic functions in its development from the pathbreaking works by L. Carleson up to the most recent achievements and in its connections with the theory of singular integral operators and Carleson-type embedding theorems, moment problems etc. · Szökefalvi-Nagy-Foias model spaces studied from the point of view of holomorphic spaces · holomorphic spaces (Hardy, Bergman, Hölder, and Sobolev spaces) · analytic functions smooth up to the boundary with their subtle properties related to the Nevanlinna-Smirnov factorization, division and multiplication, and zero sets · a new approach to weighted inequalities for singular integrals based on the Bellman function in optimization theory; · the uncertainty principle in harmonic analysis and, in particular, a complete version of Turan‘s lemma on trigonometric sums · Hankel operators and stationary Gaussian processes · Fourier multipliers, and spectral analysis of some differential operators. These themes are united by the "operator theoretic ideology" and systematic use of modern function theoretical techniques. The book is dedicated to the memory of S. A. Vinogradov. It contains a bibliographical note (with a lively portrait) of S. A. Vinogradov, a detailed survey of his mathematical achievements, and a complete list of publications, as well as the translations of two of Vinogradov‘s surveys whose Russian originals are now hardly accessible.
Bergman Spaces and Related Topics in Complex Analysis
Author: Alexander A. Borichev
language: en
Publisher: American Mathematical Soc.
Release Date: 2006
This volume grew out of a conference in honor of Boris Korenblum on the occasion of his 80th birthday, held in Barcelona, Spain, November 20-22, 2003. The book is of interest to researchers and graduate students working in the theory of spaces of analytic function, and, in particular, in the theory of Bergman spaces.